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A266516
Decimal representation of the n-th iteration of the "Rule 29" elementary cellular automaton starting with a single ON (black) cell.
2
1, 3, 4, 111, 16, 1983, 64, 32511, 256, 523263, 1024, 8384511, 4096, 134201343, 16384, 2147418111, 65536, 34359476223, 262144, 549754765311, 1048576, 8796088827903, 4194304, 140737471578111, 16777216, 2251799746576383, 67108864, 36028796750528511, 268435456
OFFSET
0,2
FORMULA
Empirical a(n) = 21*a(n-2) - 84*a(n-4) + 64*a(n-6) for n>5. - Vincenzo Librandi, Dec 31 2015 and Apr 16 2019
Empirical g.f.: (1+3*x-17*x^2+48*x^3+16*x^4-96*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)). - Colin Barker, Dec 31 2015 and Apr 16 2019
Conjecture: a(n) = 2*(4^n - 2^n) - 1 for odd n; a(n) = 2^n for even n. - Karl V. Keller, Jr., Oct 03 2021
MATHEMATICA
rule=29; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Table[FromDigits[catri[[k]], 2], {k, 1, rows}] (* Decimal Representation of Rows *)
CROSSREFS
Sequence in context: A126578 A332972 A041351 * A066496 A041465 A004124
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 30 2015
STATUS
approved